TITLE

Conservativeness, Stability, and Abstraction

AUTHOR(S)
Cook, Roy T.
PUB. DATE
September 2012
SOURCE
British Journal for the Philosophy of Science;Sep2012, Vol. 63 Issue 3, p673
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
One of the main problems plaguing neo-logicism is the Bad Company challenge: the need for a well-motivated account of which abstraction principles provide legitimate definitions of mathematical concepts. In this article a solution to the Bad Company challenge is provided, based on the idea that definitions ought to be conservative. Although the standard formulation of conservativeness is not sufficient for acceptability, since there are conservative but pairwise incompatible abstraction principles, a stronger conservativeness condition is sufficient: that the class of acceptable abstraction principles be strictly logically symmetrically class conservative. The article concludes with an examination of which classes of abstraction principles meet this criteria. 1 Introduction2 The Technical State of the Art3 Abstraction and Conservativeness4 Abstraction Stabilized5 Characterizing SLSC-Conservativeness6 Conclusion
ACCESSION #
78359877

 

Related Articles

  • Proper Efficiency and the Linear Fractional Vector Maximum Problem. Eng Ung Choo // Operations Research;Jan/Feb84, Vol. 32 Issue 1, p216 

    A vector maximum problem arises when two or more criterion functions are to be simultaneously maximized over a feasible region. We prove that, in linear fractional vector maximum problems, every efficient solution satisfies the requirements of a restricted concept of efficiency, the notion of...

  • The Short Long Life of Russell's Denoting Concepts. Costreie, Sorin // Teorema;2005, Vol. 24 Issue 3, p97 

    The paper focuses on Russell's Theory of Denoting Concepts [TDC], to see why he did both adopt and very soon abandon it. With regard to TDC, I detect three kinds of problems: ontological (the denotation of empty denoting concepts), logical (the infinite regress of meaning in the case of denoting...

  • Concepts and Recipes. Materna, Pavel // Acta Analytica;Spring2009, Vol. 24 Issue 1, p69 

    If concepts are explicated as abstract procedures, then we can easily show that each empirical concept is a not an effective procedure. Some, but not all empirical concepts are shown to be of a special kind: they cannot in principle guarantee that the object they identify satisfies the intended...

  • What Philosophy Can Do. Haldane, John // First Things: A Monthly Journal of Religion & Public Life;Nov2005, Issue 157, p22 

    Discusses the significance of philosophy in human beings. Examination of the content of concepts derived from human beings' engagement with reality; Possibility of philosophy as rational abstract reflection; Methods used by philosophers to answer questions.

  • Theoretical and methodological issues in the use of decision-making as an indicator of conjugal power: Some Canadian observations. Brinkerhoff, Merlin; Lupri, Eugen // Canadian Journal of Sociology;Winter78, Vol. 3 Issue 1, p1 

    This paper critically examines problems of measurement and conceptualization in the decision-making approach to the study of conjugal power. The empirical analysis is based on data derived from 464 separately interviewed couples in a Western Canadian city. The epistemic correlation between...

  • The logic of means-end analysis. Lane, Jan-Erik // Quality & Quantity;1986, Vol. 20 Issue 4, p339 

    The conceptual scheme of means of ends for the analysis of action in a wide sense used to be considered a basic paradigm in the social sciences. It has come under attack from various points and as a result has today lost much of its appeal and status. If some basic distinctions are introduced...

  • Intuition and Visualization in Mathematical Problem Solving. Giardino, Valeria // Topoi;Apr2010, Vol. 29 Issue 1, p29 

    In this article, I will discuss the relationship between mathematical intuition and mathematical visualization. I will argue that in order to investigate this relationship, it is necessary to consider mathematical activity as a complex phenomenon, which involves many different cognitive...

  • Against swamping. Carter, J. Adam; Jarvis, Benjamin // Analysis;Oct2012, Vol. 72 Issue 4, p690 

    The Swamping Argument – highlighted by Kvanvig (2003; 2010) – purports to show that the epistemic value of truth will always swamp the epistemic value of any non-factive epistemic properties (e.g. justification), so that these properties can never add any epistemic value to an...

  • A material dissolution of the problem of induction. Norton, John // Synthese;Mar2014, Vol. 191 Issue 4, p671 

    In a formal theory of induction, inductive inferences are licensed by universal schemas. In a material theory of induction, inductive inferences are licensed by facts. With this change in the conception of the nature of induction, I argue that the celebrated 'problem of induction' can no longer...

Share

Read the Article

Courtesy of NEW JERSEY STATE LIBRARY

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics